tìm các cặp số nguyên x,y thỏa mãn : 3xy+2x-5y=6

1 bình luận về “tìm các cặp số nguyên x,y thỏa mãn : 3xy+2x-5y=6”

1. Giải đáp + Lời giải và giải thích chi tiết:

   3xy+2x-5y=6

   =>9xy+6x-15y=18

   =>3x(3y+2)-5(3y+2)=18-10

   =>(3y+2)(3x-5)=8

   Ta có bảng sau:

   \begin{array}{|c|c|c|}\hline \text{3x-5}&\text{1}&\text{2}&\text{4}&\text{8}&\text{-1}&\text{-2}&\text{-4}&\text{-8}\\\hline \text{3y+2}&\text{8}&\text{4}&\text{2}&\text{1}&\text{-8}&\text{-4}&\text{-2}&\text{-1}\\\hline \text{3x}&\text{6}&\text{7}&\text{9}&\text{13}&\text{4}&\text{3}&\text{1}&\text{-3}\\\hline \text{3y}&\text{6}&\text{2}&\text{0}&\text{-1}&\text{-10}&\text{-6}&\text{-4}&\text{-3}\\\hline \text{x}&\text{2}&\text{$\dfrac{7}{3}$}&\text{3}&\text{$\dfrac{13}{3}$}&\text{$\dfrac{4}{3}$}&\text{1}&\text{$\dfrac{1}{3}$}&\text{-1}\\\hline \text{y}&\text{2}&\text{$\dfrac{2}{3}$}&\text{0}&\text{$\dfrac{-1}{3}$}&\text{$\dfrac{-10}{3}$}&\text{-2}&\text{$\dfrac{-4}{3}$}&\text{-1}\\\hline\end{array}

   Vì x,y in Z

   =>(x;y)={(2;2);(3;0);(1;-2);(-1;-1)}

   Trả lời